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Conformal Fields in Higher Dimensions

We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A similar analysis is

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aCERN-TH/2000-152UCLA/00/TEP/18February1,2008CONFORMALFIELDSINHIGHERDIMENSIONS*S.Ferrara andC.Frønsdal PhysicsDepartment,UniversityofCaliforniaLosAngelesCA90095-1547,USA CERNTheoreticalDivision,CH1211Geneva23SwitzerlandABSTRACT.Wegeneralize,toanyspace-timedimension,theunitarityboundsofhigh-estweightUIR’softheconformalgroupswithLiealgebrasso(2,d).Weclassifygaugetheoriesinvariantunderso(2,d),bothintegralandhalf-integralspins.Asimilaranalysisiscarriedoutforthealgebrasso (2n).Westudynewunitarymodulesoftheconformalalgebraind>4,thathavenoanalogueford≤4astheycannotbeobtainedby“squaring”singletons.Thismaysuggesttheinterpretationofhigherdimensionalnon-trivialconformal eldtheoriesastheoriesof“tensionless”p-branesofwhichtensionlessstringsind=6arejustparticularexamples.

Introduction.

ExtensiveworkonAdSd+1anditsrelationtoconformal eldtheoriesonMcd= AdSd+1hasfoundaninterestingrealizationinsupergravityandstringandMthe-orybyrelatingthehorizongeometryofp-branestotheworld-volumedynamicsofthe

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